A parallelogram and a rhombus are equal in area

Question:

A parallelogram and a rhombus are equal in area. The diagonals of the rhombus measure 120 m and 44 m. If one of the sides of the parallelogram measures 66 m, find its corresponding altitude.

Solution:

Diagonals $d_{1}$ and $d_{2}$ of the rhombus measure $120 \mathrm{~m}$ and $44 \mathrm{~m}$, respectively.

Base of the parallelogram = 66 m

Now,
Area of the rhombus = Area of the parallelogram

$\Rightarrow \frac{1}{2} \times d_{1} \times d_{2}=$ Base $\times$ Height

$\Rightarrow \frac{1}{2} \times 120 \times 44=66 \times$ Height

$\Rightarrow 60 \times 44=66 \times$ Height

$\Rightarrow 2640=66 \times$ Height

$\Rightarrow$ Height $=\frac{2640}{66}$

 

$\Rightarrow$ Height $=40 \mathrm{~m}$

Hence, the measure of the altitude of the parallelogram is 40 m.

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